Jenny has a candy business selling bags combined with chocolate, jelly beans, M&M's, Skittles, and gummy bears for $2.20, $1.70, $2.10, $3.40, and $3.10 per kg, respectively. The total fat, protein, vitamins, and sodium of each of the ingredients (in kg per pound) is summarized below, along with the calories per kg of ingredient:
Ingredient Protein Vitamins Sodium Calories
Chocolate 4 20 7 450
Jelly beans 2 10 4 160
M&M's 1 10 5 500
Skittles 10 30 9 300
Gummy bears 1 20 3 500
Jenny wants to know the cheapest way to sell bags of combined candy. The candy bags should have at least 35g of vitamins, 15g of minerals, 10g of protein, and 650 calories per two-kg package. Additionally, for each ingredient, there must be at least 5% and no more than 60% of the weight of the package.
(i) Formulate a linear programming (LP) model to determine how much of each candy should be used to produce the least costly candy bag for a two-kilogram package, showing the four steps:
Step 1: Fully understand the managerial or optimization problem being faced
Step 2: Define the decision variables
Step 3: Identify the objective function
Step 4: Identify the constraints